English
Evaluation under equivalence commutes with the transported representation.
Русский
Оценка по эквиваленции компонуется с переносимой представлением.
LaTeX
$$$F^{\\text{ofEquiv}}(a) = F(a')$ where $a'$ corresponds to a under E$$$
Lean4
/-- Map a Ctop to an equivalent representation type. -/
def ofEquiv (E : σ ≃ τ) : Ctop α σ → Ctop α τ
| ⟨f, T, h₁, I, h₂, h₃⟩ =>
{ f := fun a ↦ f (E.symm a)
top := fun x ↦ E (T x)
top_mem := fun x ↦ by simpa using h₁ x
inter := fun a b x h ↦ E (I (E.symm a) (E.symm b) x h)
inter_mem := fun a b x h ↦ by simpa using h₂ (E.symm a) (E.symm b) x h
inter_sub := fun a b x h ↦ by simpa using h₃ (E.symm a) (E.symm b) x h }
